A080035 - OEIS

A080035

"Orderly" Friedman numbers (or "good" or "nice" Friedman numbers): Friedman numbers (A036057) where the construction digits are used in the proper order.

127, 343, 736, 1285, 2187, 2502, 2592, 2737, 3125, 3685, 3864, 3972, 4096, 6455, 11264, 11664, 12850, 13825, 14641, 15552, 15585, 15612, 15613, 15617, 15618, 15621, 15622, 15623, 15624, 15626, 15632, 15633, 15642, 15645, 15655, 15656

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes in this sequence are listed in A252483. The subsequence A156954 is a simpler variant where no parentheses, unary operations (negation) nor concatenation is allowed. - M. F. Hasler, Jan 07 2015

REFERENCES

Credit goes to Mike Reid (Brown University) and Eric Friedman (Stetson University).

Colin Rose, "Radical Narcissistic numbers", J. Recreational Mathematics, vol. 33, (2004-2005), pp. 250-254. See page 251.

LINKS

Table of n, a(n) for n=1..36.

M. Brand, Friedman numbers have density 1, Discrete Applied Mathematics, Volume 161, Issues 16-17, November 2013, Pages 2389-2395.

Ed Copeland and Brady Haran, Friedman numbers, Numberphile video, 2014

Eric Friedman, Friedman Numbers.

Robert G. Wilson v, Table of n, a(n) for n = 1..108 .

EXAMPLE

127 = -1 + 2^7, 343 = (3 + 4) ^ 3, 736 = 7 + 3^6, etc.

The 4th "orderly" Friedman number is 1285 = (1 + 2^8) * 5.